What is "primary motion" and "feed motion"?

In machining, the primary motion is a rectilinear or rotational motion of a cutting tool or a workpiece that provides the tool advance toward the workpiece to ensure chip removal. In a machining process, the primary motion features the maximum speed and most of the energy, which is required for machining, when compared to all other motions. The primary motion in turning, for example, is the rotation of a workpiece, while in milling, the primary motion is the rotation of a mill.

The feed motion is a rectilinear or rotational motion of a cutting tool, which adds the primary motion to complete cutting action. This motion features significantly less speed when compared to the speed of a primary motion.

What is the difference between specific cutting forces that are designated as k_cand k_c1?

"k_c" relates to actual specific cutting force - the force that is needed to remove a material chip area of 1 mm² (.0016 in²), which has actual average chip thickness maintained in a machining process.
"k_c1" is commonly used for designating the specific cutting force to remove a material chip area of 1 mm² (.0016 in²) with 1 mm (.004 in) thickness.
However, in some technical data sources, the actual specific cutting force may be designated by "k_c1", and specific cutting force to remove a material chip area of 1 mm² (.0016 in²) with 1 mm (.004 in) thickness by "k_c1.1". Number "1" that follows index "c" relates to 1 mm² chip area, and addition "1.1" highlights "1 mm² chip area with 1 mm thickness".